diff --git a/doc/users/next_whats_new/2018_01_25_scale_axis_by_factor.rst b/doc/users/next_whats_new/2018_01_25_scale_axis_by_factor.rst
new file mode 100644
index 000000000000..0d28bbde7b22
--- /dev/null
+++ b/doc/users/next_whats_new/2018_01_25_scale_axis_by_factor.rst
@@ -0,0 +1,10 @@
+Ability to scale axis by a fixed order of magnitude
+---------------------------------------------------
+
+To scale an axis by a fixed order of magnitude, set the *scilimits* argument of
+``Axes.ticklabel_format`` to the same (non-zero) lower and upper limits. Say to scale
+the y axis by a million (1e6), use ``ax.ticklabel_format(style='sci', scilimits=(6, 6), axis='y')``.
+
+The behavior of ``scilimits=(0, 0)`` is unchanged. With this setting, matplotlib will adjust
+the order of magnitude depending on the axis values, rather than keeping it fixed. Previously, setting
+``scilimits=(m, m)`` was equivalent to setting ``scilimits=(0, 0)``.
diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index 259d70064d48..bb2b2b83c71e 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -2672,6 +2672,8 @@ def ticklabel_format(self, **kwargs):
                            be used for numbers outside the range
                            10`m`:sup: to 10`n`:sup:.
                            Use (0,0) to include all numbers.
+                           Use (m,m) where m <> 0 to fix the order
+                           of magnitude to 10`m`:sup:.
           *useOffset*      [ bool | offset ]; if True,
                            the offset will be calculated as needed;
                            if False, no offset will be used; if a
diff --git a/lib/matplotlib/tests/test_ticker.py b/lib/matplotlib/tests/test_ticker.py
index 32206a0c6168..c374c1f3f95b 100644
--- a/lib/matplotlib/tests/test_ticker.py
+++ b/lib/matplotlib/tests/test_ticker.py
@@ -228,6 +228,17 @@ class TestScalarFormatter(object):
 
     use_offset_data = [True, False]
 
+    scilimits_data = [
+        (False, (0, 0), (10.0, 20.0), 0),
+        (True, (-2, 2), (-10, 20), 0),
+        (True, (-2, 2), (-20, 10), 0),
+        (True, (-2, 2), (-110, 120), 2),
+        (True, (-2, 2), (-120, 110), 2),
+        (True, (-2, 2), (-.001, 0.002), -3),
+        (True, (0, 0), (-1e5, 1e5), 5),
+        (True, (6, 6), (-1e5, 1e5), 6),
+    ]
+
     @pytest.mark.parametrize('left, right, offset', offset_data)
     def test_offset_value(self, left, right, offset):
         fig, ax = plt.subplots()
@@ -257,6 +268,18 @@ def test_use_offset(self, use_offset):
             tmp_form = mticker.ScalarFormatter()
             assert use_offset == tmp_form.get_useOffset()
 
+    @pytest.mark.parametrize(
+        'sci_type, scilimits, lim, orderOfMag', scilimits_data)
+    def test_scilimits(self, sci_type, scilimits, lim, orderOfMag):
+        tmp_form = mticker.ScalarFormatter()
+        tmp_form.set_scientific(sci_type)
+        tmp_form.set_powerlimits(scilimits)
+        fig, ax = plt.subplots()
+        ax.yaxis.set_major_formatter(tmp_form)
+        ax.set_ylim(*lim)
+        tmp_form.set_locs(ax.yaxis.get_majorticklocs())
+        assert orderOfMag == tmp_form.orderOfMagnitude
+
 
 class FakeAxis(object):
     """Allow Formatter to be called without having a "full" plot set up."""
diff --git a/lib/matplotlib/ticker.py b/lib/matplotlib/ticker.py
index c91e78b6ae85..da9d3c6489a8 100644
--- a/lib/matplotlib/ticker.py
+++ b/lib/matplotlib/ticker.py
@@ -711,10 +711,14 @@ def _compute_offset(self):
     def _set_orderOfMagnitude(self, range):
         # if scientific notation is to be used, find the appropriate exponent
         # if using an numerical offset, find the exponent after applying the
-        # offset
+        # offset. When lower power limit = upper <> 0, use provided exponent.
         if not self._scientific:
             self.orderOfMagnitude = 0
             return
+        if self._powerlimits[0] == self._powerlimits[1] != 0:
+            # fixed scaling when lower power limit = upper <> 0.
+            self.orderOfMagnitude = self._powerlimits[0]
+            return
         locs = np.abs(self.locs)
         if self.offset:
             oom = math.floor(math.log10(range))